Depends on the class and itinerary.

Earning enough BA tier points or QF sector credits for Emerald can be easier if you take a fair number of long-haul flights in F (or A). On AA, J (D) and F (A) earn the same EQM and qualifying points as each other, so on a J-class (D) itinerary you can make Emerald (AA EXP) with the same number of BIS miles as someone sitting in first class. Whether or not you would make Emerald on the same itinerary with other airlines would depend entirely on the itinerary.

For example on a DONE3 RTW, it's very hard (almost impossible AFAIK) to make EXP without counting positioning flights (i.e. flights to/from the RTW start point) or non-RTW open-jaw connectors, etc. On BA a DONE3 might make Gold (especially if you're creative in N. America where DONExs book into A, with A tier points) but it might be a stretch; can't speak for QF.

Certainly I think the bonus/status miles on AA are more generous than the others.